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Frederic Mishkin, who’s been a professor at Columbia Business School for almost 30 years, is good at solving problems and expressing ideas. Whether he’s standing in front of a lecture hall or engaged in a casual conversation, he’s a blur of motion, his hands waving, pointing, jabbing the air. “I talk with my hands,” he says. “I always have.” When he was in graduate school, in fact, one of his professors was so exasperated by this constant gesticulating that he made the young economist sit on his hands whenever he visited the professor’s office.

It turns out, however, that Mishkin’s mentor had it exactly wrong. Gesture doesn’t hinder clear thought and speech — it facilitates it. Research demonstrates that the movements we make with our hands when we talk constitute a kind of second language, adding information that’s absent from our words. It’s learning’s secret code: Gesture reveals what we know. It reveals what we don’t know. And it reveals (as Donald Rumsfeld might put it) what we know, but don’t yet know we know. What’s more, the congruence (or lack of congruence) between what our voices say and how our hands move offers a clue to our readiness to learn.

Many of the studies establishing the importance of gesture to learning have been conducted by Susan Goldin-Meadow, a professor of psychology at the University of Chicago. “We change our minds by moving our hands,” writes Goldin-Meadow in a review of this work published in the current issue of the journal Cognitive Science. Particularly significant are what she calls “mismatches” between verbal expression and physical gestures. A student might say that a heavier ball falls faster than a light one, for example, but make a gesture indicating that they fall at the same rate, which is correct. Such discrepancies indicate that we’re in a transitional state, moving from one level of understanding to another. The thoughts expressed by hand motions are often our newest and most advanced ideas about the problem we’re working on; we can’t yet assimilate these notions into language, but we can capture them in movement. When a child employs gesture, Goldin-Meadow notes, “the information about the child’s cognitive state is conveyed sub rosa — below the surface of ordinary conversation.” Such gesture-speech mismatches have been found in toddlers going through a vocabulary spurt, in elementary-school children describing why the seasons change, and in adults attempting to explain how a machine works.

Goldin-Meadow’s more recent work shows not only that gesture is an index to our readiness to learn, but that it actually helps to bring learning about. It does so in two ways. First, it elicits helpful behavior from others around us. Goldin-Meadow has found that adults spontaneously respond to children’s speech-gesture mismatches by adjusting their mode of instruction. Parents and teachers apparently receive the signal that children are ready to learn, and they act on it by offering a greater variety of problem-solving strategies.

The act of gesturing itself also seems to accelerate learning, bringing nascent knowledge into consciousness and aiding the understanding of new concepts. A 2007 study by Susan Wagner Cook, an assistant professor of psychology at the University of Iowa, reported that third-graders who were asked to gesture while learning algebra were nearly three times more likely to remember what they’d learned than classmates who did not gesture. Another experiment conducted by Cook determined that college students who gestured as they retold short stories they’d seen recalled the details of the stories better, suggesting that gesturing as we’re remembering helps retrieve the information from memory.

So how can you crack learning’s secret code? First, pay attention to your own gestures. Research has found that watching a teacher gesture encourages young learners to produce gestures of their own. Learning improves even when children are given a specific gesture by someone else, rather than generating it themselves. In a 2009 experiment, Goldin-Meadow demonstrated that fourth-graders learning how to solve a math equation identified the correct answers more often when they imitated a helpful gesture shown to them by an adult than when they simply repeated the grown-up’s words.

Second, train yourself to attend to others’ gestures. Notice in particular the gestures that diverge from speech — when people say one thing and motion another, they are primed to take advantage of instruction and direction from others. And encourage your kids to move their hands when they talk. Studies show that children instructed to gesture make more speech-gesture mismatches — that is, they increase their readiness to learn. To those like Frederic Mishkin’s erstwhile professor, who think we should remain still while speaking, the science of learning has given us a cheeky retort: Tell it to the hand.